Learning Permutation Distributions via Reflected Diffusion on Ranks
The finite symmetric group S_n provides a natural domain for permutations, yet learning probability distributions on S_n is challenging due to its factorially growing size and discrete, non-Euclidean structure. Recent permutation diffusion methods define forward noising via shuffle-based random walks (e.g., riffle shuffles) and learn reverse transitions with Plackett-Luce (PL) variants, but the resulting trajectories can be abrupt and increasingly hard to denoise as n grows. We propose Soft-Rank Diffusion, a discrete diffusion framework that replaces shuffle-based corruption with a structured soft-rank forward process: we lift permutations to a continuous latent representation of order by...
| Authors | Sizhuang He, Yangtian Zhang, Shiyang Zhang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 18 March 2026 |
| Last updated at source | 12 June 2026 |
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